Step by step
The question
Question: write the equation for this table: x is 1, 2, 3, 4, and y is 6, 4, 2, 0.
x: 1, 2, 3, 4; y: 6, 4, 2, 0
We write it as a table.
1 Rate of change
Rate of change means: how much y changes when x goes up by 1.
y changes by −2 when x goes up by 1.
Change in y on top.
Change in x at the bottom.
= m = −21
m = change in y ÷ change in x
2 Start value
The start value is y when x is 0.
The table starts at x = 1.
We go back one step to x = 0: add 2.
y at 0 is 8.
= b = 6 + 2 = 8
Careful!
6 is y at x = 1.
The start value is y at x = 0.
Careful: not b = 6 ✗
3 Write the equation
A line is y = m x plus b: m is the rate of change, b is the start value.
y = mx + b
So the equation is y = −2x + 8.
= y = −2x + 8
4 Check
Let's check with the last pair: x = 4.
The equation gives 0.
The table says 0.
So the answer is right!
x = 4: −2 × 4 + 8 = 0
Let's look back.
First: rate of change.
Then: start value.
Then: write the equation.
Last: check.
Answer
= y = −2x + 8